Calculator For Fractions Multiplying And Division

Fraction Operation Formula:

\[ \frac{a}{b} \times \frac{c}{d} \div \frac{e}{f} = \frac{a \times c \times f}{b \times d \times e} \]

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Third Fraction Numerator (e):

Third Fraction Denominator (f):

Result:

Simplified Fraction:

Decimal Value:

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1. What is the Fraction Multiplication and Division Formula?

The formula for multiplying and dividing fractions is a fundamental mathematical operation used in various fields including science, engineering, and everyday calculations. It provides a way to combine fractional quantities through multiplication and division operations.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \frac{a}{b} \times \frac{c}{d} \div \frac{e}{f} = \frac{a \times c \times f}{b \times d \times e} \]

Where:

\( a \) — First fraction numerator
\( b \) — First fraction denominator
\( c \) — Second fraction numerator
\( d \) — Second fraction denominator
\( e \) — Third fraction numerator
\( f \) — Third fraction denominator

Explanation: The calculator first multiplies all numerators together (a × c × f), then multiplies all denominators together (b × d × e), and finally simplifies the resulting fraction by finding the greatest common divisor.

3. Importance of Fraction Operations

Details: Understanding fraction multiplication and division is essential for solving problems in algebra, physics, chemistry, and engineering. It's particularly important when dealing with ratios, proportions, and scaling factors.

4. Using the Calculator

Tips: Enter all numerator and denominator values. Denominators cannot be zero. The calculator will provide the raw result, simplified fraction, and decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: Division by zero is undefined. The calculator requires all denominators to be non-zero values.

Q2: How does the simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divides both by this value.

Q3: Can I enter negative fractions?
A: Yes, the calculator handles negative values. The sign will appear in the numerator of the simplified fraction.

Q4: What's the maximum number size it can handle?
A: The calculator uses PHP's float type, which typically handles numbers up to about 1.8e308 with precision to about 14 decimal digits.

Q5: How accurate are the decimal results?
A: Results are rounded to 4 decimal places for display, but calculations are performed with higher precision internally.